Observational constraints on the product of dark energy chemical potential and number density in out-of-equilibrium models

TL;DR

The study investigates observational constraints on the present-day product $μ_{0}n_{0}$ in out-of-equilibrium dark energy models with a particle-creation/destruction rate $Γ=3αH(a)$. By deriving thermodynamic bounds from entropy positivity and the second law and combining them with cosmological constraints under CPL and BA EoS parameterizations using Pantheon+ SN Ia, DESI DR2 BAO, and Planck CMB data, the authors find that $μ<0$ is required across scenarios, signaling phantom-like behavior. For $α>0$, only upper bounds on $μ_{0}n_{0}$ exist and support phantom tendencies; for $α<0$, both upper and lower bounds arise but compatibility is only achieved for very small $|α|$, with the limiting case $α≈-2×10^{-4}$ yielding $μ_{0}n_{0}≈-2.2^{+1.0}_{-0.7}$ GeV/m$^{3}$. The BA parameterization generally fails to produce a thermodynamic-compatible region, highlighting model dependence in the constraints and pointing to phantom dark energy as a robust outcome of the thermodynamic and observational analysis.

Abstract

In this work, we impose observational limits on the product of dark energy chemical potential, $μ$, and number density, $n$, at the present time in out-of-equilibrium models, considering that particles can be created or destroyed in the fluid at a rate $Γ=3αH(a)$, where $α$ is a constant and $H(a)\equiv\dot{a}/a$ is the Hubble parameter. We combine the bounds derived from the positivity of entropy and the second law of thermodynamics with observational constraints on the Chevallier-Polarski-Linder (CPL) and Barboza-Alcaniz (BA) parameterizations of the equation of state (EoS) of the component. We use Type Ia supernovae (SN Ia) data from Pantheon+; baryon acoustic oscillation (BAO) data from DESI DR2; and cosmic microwave background (CMB) measurements from Planck. For $α>0$ (particle creation), the thermodynamic restrictions yield only upper limits for the $μ_{0}n_{0}$ product, while in the case of $α<0$ (particle destruction) they establish both upper and lower limits, allowing for a range of values to be obtained. In both scenarios, however, we find that the chemical potential of dark energy must be negative, $μ<0$, which indicates a preference for the phantom regime. In particular, when $α<0$, it is noted that the thermodynamic bounds are simultaneously compatible only for very small absolute values of $α$, with $α=-0.0002$ being the limiting case and resulting in $μ_{0}n_{0}(α=-0.0002)=-2.2_{-0.7}^{+1.0}\,\,GeV/m^{3}$.

Figures (6)

• Figure 1: 1$\sigma$ and 2$\sigma$ confidence levels of the thermodynamic limits for two values of the parameter $\alpha$ and two redshifts in the CPL model.
• Figure 2: Probability that a given value of $\mu_0 n_0$ satisfies the thermodynamic conditions for positive values of $\alpha$ in the CPL model. The solid lines correspond to the bound of the positivity of the entropy and the dashed ones to the second law of thermodynamics.
• Figure 3: Probability that a given value of $\mu_0 n_0$ satisfies the thermodynamic conditions for negative values of $\alpha$ in the CPL model. The solid lines correspond to the bound of the positivity of the entropy and the dashed ones to the second law of thermodynamics. The dotted line represents the zero limit.
• Figure 4: Probability distributions of $\mu_0 n_0$ product for negative values of $\alpha$.
• Figure 5: 1$\sigma$ and 2$\sigma$ confidence levels of the thermodynamic limits for two values of the parameter $\alpha$ and two redshifts in the BA model.